Enhancement of spin current in Fe$_{85}$Co$_{15}$/Ni$_{80}$Fe$_{20}$ bilayers via interlayer ferromagnetic coupling

Technical Summary: Enhancement of Spin Current in Fe85Co15/Ni80Fe20 Bilayers via Interlayer Ferromagnetic Coupling

Problem Statement
Modern electronics face significant challenges regarding miniaturization, processing speed, and energy consumption. Spintronics offers a potential solution by utilizing pure spin currents to transport information, thereby reducing Joule heating losses. A primary mechanism for generating these currents is Spin Pumping (SP), where a ferromagnet (FM) driven to ferromagnetic resonance (FMR) transfers angular momentum to an adjacent normal metal. The amplitude of the injected spin current is directly proportional to the area of the magnetization precession trajectory. While Fe-Co alloys are promising candidates for the FM layer due to their low intrinsic Gilbert damping, the specific influence of interlayer exchange coupling in bilayer systems on the precession area and subsequent spin current injection requires detailed investigation.

Methodology
The study focuses on a bilayer system composed of Fe85Co15 (Fe-Co) and Permalloy (Py, Ni80Fe20) grown on MgO[100] substrates via magnetron sputtering.

• Sample Preparation: A series of bilayers were fabricated with a fixed Py thickness of 5 nm and varying Fe-Co thicknesses ranging from 5 nm to 25 nm. Reference samples with extreme thickness ratios (e.g., Fe-Co 50 nm/Py 3 nm) were also grown. Structural quality was verified using X-Ray Reflectometry (XRR) and High-Resolution Transmission Electron Microscopy (HRTEM), confirming epitaxial growth with a 45° rotation of the Fe-Co lattice relative to the MgO substrate.
• Magnetic Characterization: Static magnetic properties were analyzed using Vibrating Sample Magnetometry (VSM) and Magneto-Optical Kerr Effect (MOKE). These measurements identified the easy ([100]) and hard ([110]) magnetization axes and determined saturation magnetization ($M_s$) and coercivity.
• Dynamic Characterization: Ferromagnetic Resonance (FMR) measurements were conducted in X-band (9.7 GHz), K-band (24 GHz), and Q-band (~35 GHz) to analyze the angular dependence of the resonance field ($H_r$). Broadband FMR (3.5–19.5 GHz) was also performed along the hard axis using a Vector Network Analyzer (VNA).
• Theoretical Modeling: The experimental data were analyzed using a bilayer model based on the Landau-Lifshitz-Gilbert (LLG) equation of motion. The model incorporated Zeeman energy, shape anisotropy, cubic magnetocrystalline anisotropy (dominant in Fe-Co), uniaxial anisotropy, and interlayer exchange coupling ($J_{ex}$). The model calculated the magnetization precession components ($m_\theta, m_\phi$) and the resulting precession area ($S = \pi m_\theta m_\phi$) for both acoustic and optical modes.

Key Results

• Structural and Static Properties: The samples exhibited strong interlayer coupling, evidenced by continuous hysteresis loops without sharp breaks. The system displayed cubic magnetic anisotropy with easy axes along Fe-Co [100] and hard axes along [110]. Saturation magnetization increased with Fe-Co thickness, consistent with a thickness-weighted average of the two layers.
• FMR and Coupling: The FMR spectra revealed a single resonance peak in the X-band, indicating that the system behaves as a coupled ferromagnetic bilayer where only the in-phase (acoustic) mode is observable at these frequencies. The resonance field minima occurred at 45° relative to the field, corresponding to the Fe-Co [100] direction.
• Anisotropy and Exchange Constants: Fitting the angular dependence of $H_r$ yielded cubic anisotropy constants ($H_c$) that increased with Fe-Co thickness (ranging from ~216 Oe to ~308 Oe). The interlayer exchange constant ($J_{ex}$) was found to be approximately 1 erg/cm² across all samples, though the model could only determine a lower bound due to the proximity of the experimental resonance fields to the theoretical limit of infinite coupling.
• Precession Area and Spin Current: A critical finding is the non-monotonic behavior of the magnetization precession area as a function of $J_{ex}$. Simulations indicate that the precession area of the Py (capping) layer reaches a maximum at an intermediate exchange constant (e.g., ~0.11 erg/cm² for the hard axis).
  • At low $J_{ex}$, the layers behave independently.
  • As $J_{ex}$ increases, the torque exerted by the Fe-Co layer on the Py layer increases, enhancing the precession area.
  • At very high $J_{ex}$ (approaching a single effective material), the relative motion between layers vanishes, and the precession area decreases.
• Thickness Dependence: The maximum precession area for the Py layer increases as the Fe-Co underlayer thickness increases. Furthermore, the position of the maximum precession area shifts with the excitation frequency and the saturation magnetization of the constituent layers.

Significance and Claims
The paper demonstrates that the spin current injected from a ferromagnetic bilayer system can be optimized by tuning the interlayer exchange coupling. The authors claim that the precession area—and consequently the spin current intensity—is not maximized by simply increasing the coupling strength to its maximum, but rather at a specific intermediate value of the exchange constant.

The study suggests that this effect arises from the interplay between microwave excitation and the exchange-mediated torque between the layers. By adjusting parameters such as the exchange constant (potentially via a non-magnetic spacer), the saturation magnetization of the underlayer and capping layer, and the excitation frequency, it is possible to maximize the magnetization precession trajectory. This provides a pathway to enhance spin injection efficiency and improve the energy efficiency of spin-current generation devices, without proposing specific new applications beyond the optimization of the generation mechanism itself.